A Closed Form Expression for the Form Factor between Two Polygons

Abstract:

Form factors are used in computer graphics and radiative heat transfer to
describe the fraction of diffusely refledted light or radiation leaving one
surface and arriving at another. They are a fundamental geometric property
used for computation. Many special configurations admit closed form solutions.
However, the important case of the form factor between two polygons in three
space has had no known closed form solution. We give a closed form solution
for the case of general (planar, convex, or concave, possibly containing holes)
polygons. The solution is non-elementary since it involves dilogarithms.